Find the wrong number in the series: 5, 15, 30, 135, 405, 1215, 3645

Introduction / Context:
This series is intended to be a clean “multiply by 3” chain. One term violates the constant ratio, and catching that restores the simple geometric progression.

Given Data / Assumptions:

• Given: 5, 15, 30, 135, 405, 1215, 3645.
• Ideal 3× progression: 5, 15, 45, 135, 405, 1215, 3645.

Concept / Approach:
Compute ratios term by term. A constant ratio of 3 should connect successive terms. Any deviation indicates the wrong entry.

Step-by-Step Solution:
15 / 5 = 3 (OK)30 / 15 = 2 (should have been 3) ✗135 / 45 = 3 (if 45 had been present)405 / 135 = 31215 / 405 = 33645 / 1215 = 3

Verification / Alternative check:
Replacing 30 with 45 yields a perfect geometric sequence with ratio 3. All later terms already adhere to the 3× rule.

Why Other Options Are Wrong:

• 405 / 1215 / 3645 are consistent 3× successors; removing any would break the clean ratio.

Common Pitfalls:

• Overlooking a single early error and trying to fit mixed ratios thereafter. The simplest constant ratio is preferable.

Final Answer:
30